• Abstract

In this paper we prove that the Gromov-Hausdorff distance between $\mathbb{R}^n$ and its subset $A$ is finite if and only if $A$ is an $ε$-net in $\mathbb{R}^n$ for some $ε>0.$ For infinite-dimensional Euclidean spaces this is not true. The proof is essentially based on upper estimate of the Euclidean Gromov-Hausdorff distance by means of the Gromov-Hausdorff distance.

• General Summary

• Abstract

All complex 3-dimensional nilalgebras were described. As a corollary, all degenerations in the variety of complex 3-dimensional nilalgebras were obtained.

• General Summary